Precalculus Examples

$\log_{b} (\frac{a^{5} c^{2}}{d^{6}})$

Step 1

Rewrite $\log_{b} (\frac{a^{5} c^{2}}{d^{6}})$ as $\log_{b} (a^{5} c^{2}) - \log_{b} (d^{6})$ .

$\log_{b} (a^{5} c^{2}) - \log_{b} (d^{6})$

Step 2

Expand $\log_{b} (d^{6})$ by moving $6$ outside the logarithm.

$\log_{b} (a^{5} c^{2}) - (6 \log_{b} (d))$

Step 3

Multiply $6$ by $- 1$ .

$\log_{b} (a^{5} c^{2}) - 6 \log_{b} (d)$

Step 4

Rewrite $\log_{b} (a^{5} c^{2})$ as $\log_{b} (a^{5}) + \log_{b} (c^{2})$ .

$\log_{b} (a^{5}) + \log_{b} (c^{2}) - 6 \log_{b} (d)$

Step 5

Expand $\log_{b} (a^{5})$ by moving $5$ outside the logarithm.

$5 \log_{b} (a) + \log_{b} (c^{2}) - 6 \log_{b} (d)$

Step 6

Expand $\log_{b} (c^{2})$ by moving $2$ outside the logarithm.

$5 \log_{b} (a) + 2 \log_{b} (c) - 6 \log_{b} (d)$